Big BOSS science overview Uros Seljak LBNLUC Berkeley
Big. BOSS science overview Uros Seljak LBNL/UC Berkeley LBNL, Nov 18, 2009
Focus of this talk • Recent progress in large scale structure: weak lensing, galaxy clustering, cluster abundance, Lyman alpha forest • A few representative applications: neutrino mass, primordial non-gaussianity, dark energy • Future directions Collaborators: P. Mc. Donald, R. Mandelbaum, N. Padmanabhan, C. Hirata, R. Reyes, A. Slosar…
Big questions in cosmology 1) Nature of acceleration of the universe: 2) dark energy 3) modification of gravity 4) something else? 5) 2) Initial conditions for structure in the Universe: 6) Inflation (of many flavors) or alternatives? 7) 3) Nature of matter (dark matter, neutrino mass…) 8) Big. BOSS can test all of these!
How to answer them? 1) 2) 3) 4) Classical tests: dark energy: redshift-distance relation: BAO and AP Growth of structure: dark energy, neutrino mass etc: need amplitude of perturbations, ie bias: weak lensing, redshift space distortions Scale dependence of clustering: primordial power spectrum, primordial non-gaussianity: need to understand scale dependence of bias Comparing the above tracers, e. g. , lensing versus redshift-space distortions: differentiates between dark energy and modified gravity theories
Scale dependence of cosmological probes WMAP CBI ACBAR Lyman alpha forest SDSS Galaxy clustering Weak lensing Cluster abundance Complementary in scale and redshift
Sound Waves • Each initial overdensity (in DM & gas) is an overpressure that launches a spherical sound wave. • This wave travels outwards at 57% of the speed of light. • Pressure-providing photons decouple at recombination. CMB travels to us from these spheres. • Sound speed plummets. Wave stalls at a radius of 150 Mpc. • Seen in CMB as acoustic peaks • Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies. Preferred separation of 150 Mpc.
A Standard Ruler • • • The acoustic oscillation scale depends on the matter-toradiation ratio (Wmh 2) and the baryon-to-photon ratio (Wbh 2). The CMB anisotropies measure these and fix the oscillation scale. In a redshift survey, we can measure this along and across the line of sight. • Yields H(z) and DA(z)! • Big. BOSS predictions: see follow-up talks • Their ratio: Alcock-Paczynski effect dr = DAdq dr = (c/H)dz Observer
Shape and acoustic oscillations in the Matter Power Spectrum • • Linear regime matter power spectrum Shape determined by matter and baryon density, primordial slope Amplitude not useful (bias) Peaks are weak; suppressed by a factor of the baryon fraction. Higher harmonics suffer from nonlinear damping.
Weighing neutrinos • • • Neutrino free streaming inhibits growth of structure on scales smaller than free streaming distance If neutrinos have mass they contribute to the total matter density, but since they are not clumped on small scales dark matter growth is suppressed For m=0. 1 -1 e. V free-streaming scale is >>10 Mpc Neutrinos are quasi-relativistic at z=1000: effects on CMB also important (anisotropic stress etc) opposite sign, unique signature! m=0. 15 x 3, 0. 3 x 3, 0. 6 x 3, 0. 9 x 1 e. V
Galaxy bias determination • Galaxies are biased tracers of dark matter; the bias is believed to be scale independent on large scales (k<0. 1/Mpc) • If we can determine the bias we can use galaxy power spectrum and relate it to the dark matter spectrum • redshift space disortions • bispectrum • Weak lensing
Redshift space distortions • Usual approach: measure power along the radial direction and compare to power along transverse direction to determine beta • Need linear regime, limited by sampling variance due to finite number of large scale structures, each of which is a random gaussian realization • Lower bias higher beta: good for BIGBOSS
Redshift space Correlation Function a=0 kms-1 a=500 kms-1 =0 (along the l. o. s. ) =0 kms-1 =0. 4 a= 500 kms 1 =0. 4 (perpendicular to the l. o. s. ) Hawkins et al. (2003, MNRAS, 346, 78)
Beta reconstruction of LRGs: quadrupole to monopole ratio (N-body simulations) Reyes etal 2009
Sources of error in galaxy surveys • Sampling (cosmic) variance: each structure (mode in Fourier space) is a random variable, error on the power spectrum) is , where N is the number of modes measured. This is a problem for BAO, need large volume • Shot noise: with a small number of galaxies individual structures (modes) will not be measured precisely; usual assumption: Poisson process where shot noise is where is the number density of galaxies (this can be improved upon) • Relative contribution: • For BAO we want shot noise error=sampling error • For RSD one gains as shot noise decreases
How to reduce cosmic variance? • Two tracers: Mc. Donald & US 2008 • Take the ratio • Density perturbation drops out, so no cosmic variance • Transverse vs radial allows to determine bias ratio and beta separately • Full angular dependence: AP geometrical test • What limits the measurement is shot noise and stochasticity: unclear if Big. BOSS can take advantage of this method (number density low, no high bias tracer)
Velocity divergence power spectrum Growth of structure to 0. 1% This is potentially better than other probes of growth (weak lensing, cluster abundance)
Can one reduce shot noise? Possibly! Uniform weighting Mass weighting 10 x reduction in noise relative to signal! US, Hamaus, Desjacques 2009 • One can reduce shot noise OR we can achieve the same errors by measuring redshifts of several times fewer galaxies • Need all of the halos above certain mass • Emission line galaxies in Big. BOSS are not picking out all of the most massive halos
Scale dependent bias • Current analyses use Q model (Cole etal), no physical motivation, just a fitting formula • A better model has been developed by P. Mc. Donald (2008) based on (renormalized) perturbation theory and local bias ansatz • Seems to work well in simulations (Jeong & Komatsu 2008) • One result from these analyses: there is a sweet spot where scale dependent bias vanishes at second order, roughly at b=1. 7 (but still need to account for shot noise term which is not 1/n)
Weak Gravitational Lensing Distortion of background images by foreground matter Unlensed Lensed
Galaxy-dark matter correlations: galaxy-galaxy lensing + dark matter around galaxies induces tangential distortion of background galaxies + Specially useful if one has redshifts of foreground galaxies (Big. BOSS!): express signal in terms of projected surface density and transverse separation r +: not sensitive to intrinsic alignments (with photozs for source galaxies)
Simulations: dark matter reconstruction Baldauf, US, Smith (2009) Nonlinear Use simulations with realistic HOD galaxy model to model galaxies Cross-correlation coefficient r nearly unity Dark matter power spectrum reconstruction from galaxy power spectrum and galaxyshear power spectrum unbiased
Dark matter clustering reconstruction Alternative method to determine growth rate with different systematics than shear-shear correlations and more statistical power! Big. BOSS can be combined with Pan. STARRS, LSST or something else This method could blow away shear -shear correlations if the systematics are not solved (likely for the ground based WL surveys)
Ly-alpha forest as a tracer of dark matter and dark energy Basic model: neutral hydrogen (HI) is determined by ionization balance between recombination of e and p and HI ionization from UV photons (in denser regions collisional ionization also plays a role), this gives Recombination coefficient depends on gas temperature Neutral hydrogen traces overall gas distribution, which traces dark matter on large scales, with additional pressure effects on small scales (parametrized with filtering scale k. F) Fully specified within the model, no bias issues
BAO with Lyman alpha Mc. Donald and Eisenstein 2007 Big. BOSS predictions: TBD (see subsequent talks)
Non-gaussianity • • • Local model Simple single field inflation predicts fnl<<1 Nonlinear corrections give fnl around 1 More complicated inflationary models can give fnl>>1 Ekpyrotic/cyclic models generically give fnl>>1 Other models give different angular dependence of bispectrum (e. g. equilateral in DBI model, Silverstein…) • Shows up in galaxy clustering as a scale dependent bias
Effect proportional to (bias-1): need high bias tracers Dalal etal 2007 b=3. 5
How to improve these limits? US 2008 • Effect scales as (b-1), ie no effect for b=1 • On large scales limited by cosmic variance: finite number of large scale patches (modes), which are gaussian random realizations, but we need to measure average power • Two tracers: • Take the ratio • Density perturbation drops out, so no cosmic variance! • This could give error on fnl around unity with Big. BOSS if we have a biased tracer (b>1)!
Which method is best? We don’t know! Mc. Donald & US 2009 Redshift space distortions (including AP, BAO) give larger improvements than weak lensing or BAO alone BAO is a safe bet but other methods could be better (lessons from SDSS: build the most general purpose survey as possible)
Combining the methods • By combining velocity measurements (b) of LRGs with weak lensing measurement of the SAME objects we can eliminate the dependence on the amplitude of fluctuations and bias Zhang etal 2007
Testing modifications of gravity with EG Reyes, Mandelbaum, US, Gunn, Baldauf, Lombriser, in prep SDSS: 6 sigma detection In agreement with LCDM Data disagree with Te. Ve. S (aka MOND) f(R) about 1 sigma below the data: future data should be able to constrain it better Big. BOSS predictions depend on WL data
Conclusions • Big. BOSS can answer fundamental questions through a number of techniques, including galaxy clustering (BAO, RSD, AP, shape and amplitude), weak lensing and their cross-correlations, and Ly-alpha forest • Best constraints achieved by combining multiple techniques: this is also needed to test robustness of the results against systematics. • Dark energy, modifications of gravity, primordial spectrum, neutrino mass, non-gaussianity will all be studied with Big. BOSS
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